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A Third-Order Accurate Wave Propagation Algorithm for Hyperbolic Partial Differential Equations

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Abstract

We extend LeVeque’s wave propagation algorithm, a widely used finite volume method for hyperbolic partial differential equations, to a third-order accurate method. The resulting scheme shares main properties with the original method, i.e., it is based on a wave decomposition at grid cell interfaces, it can be used to approximate hyperbolic problems in divergence form as well as in quasilinear form and limiting is introduced in the form of a wave limiter.

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Authors and Affiliations

  1. Institute of Mathematics, Heinrich-Heine-University Düsseldorf, Düsseldorf, Germany

    Christiane Helzel

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  1. Christiane Helzel
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Correspondence to Christiane Helzel.

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This work was supported by the DFG through HE 4858/4-1.

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Helzel, C. A Third-Order Accurate Wave Propagation Algorithm for Hyperbolic Partial Differential Equations. Commun. Appl. Math. Comput. 2, 403–427 (2020). https://doi.org/10.1007/s42967-019-00056-3

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  • DOI: https://doi.org/10.1007/s42967-019-00056-3

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